Enumerative Combinatorics

by Charalambos A. Charalambides

Overview

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

Product Details

ISBN-13:	9781351989633
Publisher:	CRC Press
Publication date:	10/08/2018
Series:	Discrete Mathematics and Its Applications
Sold by:	Barnes & Noble
Format:	eBook
Pages:	632
File size:	2 MB

About the Author

Charalambides, Charalambos A.

Table of Contents

Basic Counting Principles. Permutations and Combinations. Factorials, Binomial and Multinomial Coefficients. The Principle of Inclusion and Exclusion.Permutations with Fixed Points and Successions. Generating Functions. Recurrence Relations. Stirling Numbers. Distributions and Occupancy. Partitions of Integers. Partition Polynomials. Cycles of Permutations. Equivalence Classes.Runs of Permutations and Eulerian Numbers. Hints and Answers to Exercises. Bibliography. Index.

Editorial Reviews

Charalambides (mathematics, U. of Athens, Greece) presents a textbook for introductory to intermediate courses in enumerative combinatorics. Beginning with the basic counting principles of addition and multiplication and continuing on to more complicated matters, chapters cover permutations and combinations; factorials, binomial, and multinomial coefficients; the principle of inclusion and exclusion; permutations with fixed points and successions; generating functions; recurrence relations; Stirling numbers; distributions and occupancy; partitions of integers; partition polynomials; cycles of permutations; equivalence classes; and runs of permutations and Eulerian numbers. Annotation c. Book News, Inc., Portland, OR (booknews.com)

"The broad field of applications of combinatorial methods makes this book useful to anyone interested in operations research, physical, or social sciences. Provides a comprehensive coverage of enumerative combinatorics, and gives many illuminating examples and interesting historical notes students of combinatorics will find the book very useful as there are many theorems, all with complete proofs, and many exercises with hints and answers." -Journal of the Operational Research Society, Vol 55, no. 2, 2004

From the Publisher